NEW YORK—Wall Street paused after a huge two-session rally Tuesday but closed mostly higher, holding on to almost all its gains even after disappointing reports on consumer sentiment and the housing market.

Stocks pulled past profit-taking that was due in part to the Conference Board’s report that consumer confidence sank to a five-year low in March. The index has been weakening since July, and is closely watched to determine the future of consumer spending, perhaps the most critical part of the economy.

Meanwhile, the Standard & Poor’s/Case-Shiller home price index ind...

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